Field of the Invention
The present invention relates to a semiconductor device. Particularly, the invention is suited for use in a semiconductor device that simulates interactions between spins of a large-scale Ising model.
Description of Related Art
Various physical phenomena and social phenomena can be expressed with interaction models. An interaction model is a model defined by a plurality of nodes constituting the model and interactions between the nodes, and bias for each node if necessary. Various models are suggested in physics and social science, but any of them can be interpreted as one form of interaction models. Furthermore, as an example of characteristics of the interaction model, influences between the nodes are limited to interactions between two nodes (interactions between two bodies). For example, considering dynamics of planets in outer space, it can be interpreted as one type of interaction model as there are interactions by universal gravitation between the nodes which are the planets; however, influences between the planets are not limited to those between two planets and three or more planets influence each other and exhibits complicated behaviors (thereby causing problems such as so-called “three-body problems” or “N-body problems”).
In the world of biology, a neural network which models a brain can be listed as an example of the interaction model. The neural network has artificial neurons, which simulate nerve cells, as nodes and there are interactions called synaptic connections between the artificial neurons. Also, a bias may be given to each neuron. Regarding the world of social science, for example, if you think about human communications, you could easily understand that there are nodes called humans and interactions composed of languages and communications. Also, it is easily imaginable that each human has its individual bias. Accordingly, there is a study to try clarifying properties, of the human communications by simulating them as an interaction model (for example, Japanese Patent Application Laid-Open (Kokai) Publication No. 2012-217518).
On the other hand, an Ising model can be an example of a representative interaction model in the world of physics. The Ising model is a model of statistical dynamics to explain behaviors of a magnetic substance. The Ising model is defined by spins having two values, that is, +1/−1 (or 0/1 or up/down), an interaction coefficient indicative of an interaction between the spins, and an external magnetic field coefficient for each spin.
Energy of the Ising model at the relevant time can be calculated from a spin alignment, the interaction coefficient, and the external magnetic field coefficient which are defined. An energy function of the Ising model can be generally represented by the following expression.
                              [                      Math            .                                                  ⁢            1                    ]                ⁢                                                                                                E          ⁡                      (            s            )                          =                              -                                          ∑                                  i                  <                  j                                                                                              ⁢                                                J                                      i                    ,                    j                                                  ⁢                                  σ                  i                                ⁢                                  σ                  j                                                              -                                    ∑              i                        ⁢                                          h                i                            ⁢                              σ                i                                                                        (        1        )            
Incidentally, σi and σj represent i-th and j-th spin values, respectively; Ji, j represents the interaction coefficient between the i-th and j-th spins; hi represents the external magnetic field coefficient for the i-th spin; and σ represents the spin alignment.
A first term of expression (1) is to calculate energy attributable to the interaction between the spins. Generally, the Ising model is expressed as an undirected graph and does not distinguish between an interaction from the i-th spin to the j-th spin or an interaction from the j-th spin to the i-th spin. Therefore, the first term calculates the influence of the interaction coefficient with respect to a combination of σi and σj that satisfy i<j. Also, a second term is to calculate energy attributable to the external magnetic field for each spin.
A ground-state search of the Ising model is an optimization problem to find a spin alignment that minimizes the energy function of the Ising model. It is known that when the range of the interaction coefficient and the external magnetic field coefficient is not limited, finding the ground state of the Ising model whose topology becomes a nonplanar graph is an NP-hard problem.
The ground-state search of the Ising model is used not only to explain behaviors of a magnetic substance which is originally a target of the Ising model, but also for various uses. This can be because the Ising model is the simplest model based on interactions and also has the capability to express various phenomena attributable to interactions. For example, Japanese Patent Application Laid-Open (Kokai) Publication No. 2012-217518 discloses a method for estimating the degree of stress in a group such as a workplace organization by using the ground-state search of the Ising model.
Furthermore, the ground-state search of the Ising model also deals with a maximum cut problem known as an NP-hard graph problem. Such a graph problem is widely applicable to, for example, community detection in social networks and segmentation for image processing. Therefore, any solver that performs the ground-state search of the Ising model can be applied to such various problems.
Since finding the ground state of the Ising model is an NP-hard problem as described above, solving the problem with von Neumann computers is difficult in terms of calculation time. While an algorithm that introduces heuristics to increase the speed is suggested, there is suggested a method of finding the ground state of the Ising model at high speeds, without using the von Neumann computers, by calculation that utilizes physical phenomena more directly, that is, by using analogue computers (for example, WO2012/118064).
Such a device requires alignment corresponding to a problem to be solved. In a case of the Ising model, elements that represent each one of spins and an interaction between the relevant spin and another spin (hereinafter referred to as the “element units”) are required corresponding to the number of spins in the Ising model for which the ground state should be searched. For example, with the device disclosed in WO 2012/118064, spins are associated with lasers and, therefore, lasers whose quantity is proportionate to the number of spins are required. In other words, high scalability that enables mounting of numerous element units is required.
In consideration of the above-described circumstances, the ground-state search of the Ising model should preferably be performed with a solid-state component such as a semiconductor device that can be implemented by regularly arranging numerous element units. Particularly, it is desirable that such a solid-state component has an array structure represented by a storage apparatus such as a DRAM (Dynamic Random Access Memory) or an SRAM (Static Random Access Memory) and the element unit has a simple structure to enhance accumulation ability. Therefore, in recent years, the applicant of the present application has been developing such semiconductor devices (semiconductor chips).
Meanwhile, in order to construct such a semiconductor device, for example, a semiconductor device that simulates interactions between spins of a large-scale Ising model, it is necessary to mount as many element units as the number corresponding to the number of spins on the semiconductor chip. Such a semiconductor device has a large chip size and its manufacturing cost is high. Therefore, in order to implement such a semiconductor device, it is desirable to construct the semiconductor device by connecting a plurality of semiconductor chips which are equipped with a certain number of element units.
However, if such a method is employed, a wiring amount between the semiconductor chips increases, thereby causing problems of an increase of the manufacturing cost and the occurrence of difficulty in implementation.
The present invention was devised in consideration of the above-described circumstances and aims at suggesting a semiconductor device that can simulate interactions between nodes of a large-scale interaction model and can be easily manufactured at inexpensive cost.